ZomeTeach Idea Exchange: Learning in Multiple Dimensions


A new school year is well underway for many of us. Classrooms are buzzing with learners, eager to find out the school year has in store for them. And teachers are jumpstarting “norms” for student engagement with and learning in mathematics. Undoubtedly, these norms will shape how students “see” themselves as participants in, contributors to, and successful learners of mathematics.

For me, an important message, or norm I want students to embrace is:

Making sense of mathematics means Creating, Connecting, and Communicating.

Making sense of mathematics means Creating, Connecting, and Communicating

Too often, students today experience mathematics as a tedious collection knowledge and procedures, and learning as a “get it” or “don’t get it” endeavor. The gap between school mathematics and mathematics as applied and practiced in the real world is often substantial.

 Closing this gap stems, in part, from privileging the multidimensional aspects of mathematics and learning mathematics. In classrooms, this means that we will make sense of mathematics by innovating, surfacing, and “playing” with ideas. We will learn to “see” patterns and relationships in the world, its structures, its dimensions, and its possibilities in many different ways. And we will work together to develop, justify, and refine mathematical ideas, explanations, and arguments. These notions underpin powerful expectations that shape what students will learn, how they will learn, and how they will demonstrate learning and growth.

Ready to Create, Connect, and Communicate? Check out the following Zometool task:


Arrange students in teams of 2-3. Provide each team a pre-assembled kit of 3 nodes, 40 blue struts, 20 yellow struts, and 20 red struts (all one length).

• Prompt each student to look at the node and make at least two observations. Elicit student ideas. Any ideas of why the node might be designed this way? What questions do we have?

• Challenge each team to develop at least 3 strategies for figuring out:


- How many triangular holes are there in a Zometool node?
- How many rectangular holes are there in a Zometool node?
- How many pentagonal holes are there in a Zometool node?
- How many total holes are there in a Zometool node?
- For the answers to these questions, click here

Task Follow-Up

  • • Questions:
    • (1) What strategies did you find for counting the total number of holes in a Zometool node?
    • (2) What types of patterns or relationships did you find and how?
  • • Prompt teams to develop, justify, and share an argument for the BEST strategy for counting the total number of holes in a Zometool node.
  • • Look for individual student strengths during this process, and have students reflect on the same (e.g., generating ideas, asking questions, representing ideas, critiquing ideas, communicating an argument, etc.)

Join the Conversation:

What types of norms for learning are you creating in your courses? How are you making these norms visible?

Send your thoughts to: zometoolamy@gmail.com